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Facility Location (cooperative Game)
The cooperative facility location game is a cooperative game of cost sharing. The goal is to share the cost of opening new facilities between the clients enjoying these facilities.Kamal Jain and Mohammad Mahdian, "Cost Sharing". Chapter 15 in The game has the following components: * There are several consumers who need a certain service, e.g, electricity connection. * There are several locations where facilities (e.g. power-stations) can be built. * For every pair of consumer (C) and location (L), there is a fixed cost of serving C from L (e.g, depending on the distance between the power station and the consumer's house). This cost is denoted Cost ,L * The cost of serving a group of consumers is lower than the sum of the cost of serving each consumer alone. EXAMPLE: * There are two facilities, F1 which costs 2 and F2 which costs 2. * There are three consumers, Alice Bob and Carl. * Alice can be served only from F1, with cost 2. So the cost of serving her alone is 2+2=4. * Bob can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Game Theory
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of Player (game), players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be Self-enforcing agreement, self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional Non-cooperative game, non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cost Sharing
In health care, cost sharing occurs when patients pay for a portion of health care costs not covered by health insurance. The "out-of-pocket" payment varies among healthcare plans and depends on whether or not the patient chooses to use a healthcare provider who is contracted with the healthcare plan's network. Examples of out-of-pocket payments involved in cost sharing include copays, deductibles, and coinsurance. In accounting, cost sharing or matching means that portion of project or program costs not borne by the funding agency. It includes all contributions, including cash and in-kind, that a recipient makes to an award. If the award is federal, only acceptable non-federal costs qualify as cost sharing and must conform to other necessary and reasonable provisions to accomplish the program objectives. Cost sharing effort is included in the calculation of total committed effort. Effort is defined as the portion of time spent on a particular activity expressed as a percentage of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Core (game Theory)
In cooperative game theory, the core is the set of feasible allocations that cannot be improved upon by a subset (a ''coalition'') of the economy's agents. A coalition is said to ''improve upon'' or ''block'' a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first except that every member of the coalition has a different consumption bundle that is part of an aggregate consumption bundle that can be constructed from publicly available technology and the initial endowments of each consumer in the coalition. An allocation is said to have the ''core property'' if there is no coalition that can improve upon it. The core is the set of all feasible allocations with the core property. Origin The idea of the core already appeared in the writings of , at the time referred to as the ''contract curve''. Even though von Neumann and Morgenstern considered it an interesting concept, they only worked with zero-sum ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bondareva–Shapley Theorem
The Bondareva–Shapley theorem, in game theory, describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game in characteristic function form. Specifically, the game's core is non-empty if and only if the game is ''balanced''. The Bondareva–Shapley theorem implies that market games and convex games have non-empty cores. The theorem was formulated independently by Olga Bondareva and Lloyd Shapley in the 1960s. Theorem Let the pair \langle N, v\rangle be a cooperative game in characteristic function form, where N is the set of players and where the ''value function'' v: 2^N \to \mathbb is defined on N's power set In mathematics, the power set (or powerset) of a set is the set of all subsets of , including the empty set and itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is po ... (the set of all subsets of N). The core of \langle N, v \rangle is non-em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Facility Location (optimization Problem)
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis. Minimum facility location A simple facility location problem is the Weber problem, in which a single facility is to be placed, with the only optimization criterion being the minimization of the weighted sum of distances from a given set of point sites. More complex problems considered in this discipline include the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. In a basic formulation, the facility location problem consists of a set of potential facility sites ''L'' where a facility can be opened, and a set of demand points ''D'' th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Facility Location (competitive Game)
The competitive facility location game is a kind of competitive game in which service-providers select locations to place their facilities in order to maximize their profits.Eva Tardos and Tom Wexler, "Network Formation Games". Chapter 19 in The game has the following components: * There are several consumers who need a certain service, e.g, electricity connection. * There are several producers that can supply this service, e.g, electricity companies. * Each producer can build its facility (e.g, a power station) in one of several locations. * For every pair of consumer (C) and location (L), there is a fixed cost of serving C from L (e.g, depending on the distance between the power station and the consumer's house). This cost is denoted Cost ,L The game is a sequential game with three steps: # Each producer selects a location for placing its facility. # Each producer set a price for each user (price discrimination is allowed, since there is a different cost for serving different cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cost-sharing Mechanism
In economics and mechanism design, a cost-sharing mechanism is a process by which several agents decide on the scope of a public product or service, and how much each agent should pay for it. Cost-sharing is easy when the marginal cost is constant: in this case, each agent who wants the service just pays its marginal cost. Cost-sharing becomes more interesting when the marginal cost is not constant. With increasing marginal costs, the agents impose a negative externality on each other; with decreasing marginal costs, the agents impose a positive externality on each other (see example below). The goal of a cost-sharing mechanism is to divide this externality among the agents. There are various cost-sharing mechanisms, depending on the type of product/service and the type of cost-function. Divisible product, increasing marginal costs In this setting, several agents share a production technology. They have to decide how much to produce and how to share the cost of production. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |